Discrete Fourier Transform
The limitations of Discrete Time Fourier Transform (DTFT) are overcome by Discrete Fourier Transform (DFT). DFT evaluates enough frequency components of the signal that are required for its reconstruction and hence is the frequency sampled version of DTFT.
In this experiment, we made use of arrays to
store the real and imaginary parts of the signal. Also the count of number of Real Addition and
Real Multiplication for N=4 and N=8 was verified.
By manipulating the signal in different ways, it
was observed that expansion of signal in time domain results in compression in
the frequency domain.
The major contribution of DFT is in the area of spectral analysis of systems.
What are the applications of DFT?
ReplyDeleteAs mentioned above, Dft has applications in spectral analysis of systems. Calculation of convolution of signals, data compression, multiplication of large polynomials, noise removal are some of its application.
DeleteBut can we rely on DFT for faster computational results ?
ReplyDeleteNo, We can't. We have a different algorithm of FFT for fast computational results.
Deletewell written
ReplyDeleteThanks:)
DeleteIs DFT computationally very efficient?
ReplyDeleteNo, DFT is not a computationally efficient method.
DeleteHow would you justify DFT not being computationally efficient?
ReplyDeleteSince the number of real and imaginary calculations required to compute DFT is more than FFT.
DeleteHow to find the no of real and imaginary multiplications?
ReplyDeleteThe number of real and imaginary multiplication is given by the formula 4N^2 and N^2 respectively.
Delete